Semiconductor pressure sensor

ABSTRACT

A semiconductor pressure sensor for measuring an external pressure exerted on the sensor, comprises a membrane, and a bridge comprising a first and a second resistor pair, arranged on a first resp. second side portion of the membrane. The first resistor pair comprises a first and a second resistor (R 1 , R 2 ) comprising elongated piezo-resistive strips connected in series, and located closely together, such that R 1  and R 2  have substantially the same temperature. The sensor has a reduced sensitivity to: a temperature gradient over the membrane, and optionally also a non-uniform stress gradient caused by packaging and a inhomogeneous disturbing electric field perpendicular to the sensor. The piezo-resistive strips of the first and second resistor may be oriented in orthogonal directions of maximum piezo-resistive coefficients. A second bridge may be added outside the membrane, for compensating for package pressure.

FIELD OF THE INVENTION

The present invention relates to the field of pressure sensors, inparticular pressure sensors integrated in a semiconductor-device.

BACKGROUND OF THE INVENTION

Semiconductor pressure sensors are known in the art.

U.S. Pat. No. 4,672,411 (Hitachi) discloses a pressure sensor (shown inFIG. 1) having a diaphragm formed in a semiconductor body, the diaphragmhaving a pair of pressure sensing semiconductor strips in a majorsurface thereof (vertical piezo-resistive strips 30, 31 in FIG. 1). Eachof the strips 30, 31 is connected at one end to the other one by asemiconductor region (triangular region 32 in FIG. 1). The semiconductorregion 32 is formed in a direction of small piezo-resistivecoefficients, while the strips 30, 31 are formed in a direction of largepiezo-resistive coefficients. The semiconductor region 32 (triangle) hasa smaller sheet resistance than the resistance of the strips 30, 31.Also, electrode lead-out regions are provided at the other ends of thestrips 30, 31, which regions have low resistance, extend in a directionof small piezo-resistive coefficients, and extend beyond the edge of thediaphragm so the electrodes contact the semiconductor body outside thediaphragm. The resistive strips 30, 31 are connected in a bridge.Deformation of the diaphragm causes the diffused resistor layers (i.e.the piezo-resistive strips) to expand or shrink so as to change theirresistances. The pressure sensor senses a pressure change byelectrically detecting the change of the resistances.

However, this pressure sensor is not very accurate in all circumstances,e.g. in case of temperature fluctuations, and in case of residualpackage-stress.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a good semiconductorpressure sensor.

In particular, it is an object of embodiments of the present inventionto provide a pressure sensor with a good accuracy, in particular in caseof a non-uniform temperature of the semiconductor substrate and/or incase of non-uniform packaging-stress and/or in case of a non-uniformelectric field, or combinations thereof.

It is an advantage of embodiments of the present invention that goodaccuracy, e.g. improved accuracy is provided, even in the presence of anon-uniform temperature and/or a non-uniform stress and/or a non-uniformelectric field, and even when said temperature, stress or field variesover time.

It is an object of particular embodiments of the present invention toprovide a semiconductor pressure sensor with an improved zero-offsetcompensation.

These objectives are accomplished by a device according to embodimentsof the present invention.

In a first aspect, the present invention provides a semiconductorpressure sensor for measuring an external pressure exerted on thesensor, comprising: a membrane as part of a semiconductor substrate forbeing deformed due to the external pressure, the membrane having amembrane edge and a membrane thickness; a first bridge circuitcomprising a first resistor pair located on or adjacent to a first sideportion of the membrane, and a second resistor pair located on oradjacent to a second side portion of the membrane; the first resistorpair comprising a first resistor connected between a first bias node anda first output node, and a second resistor connected between the firstoutput node and a second bias node; the second resistor pair comprisinga third resistor connected between the first bias node and a secondoutput node, and a fourth resistor connected between the second outputnode and the second bias node; at least one of the first and second andthird and fourth resistor comprising one or more elongatedpiezo-resistive strips arranged for measuring deformation of themembrane due to the external pressure to be measured; wherein the ratioof a largest distance between a point of the first resistor and a pointof the second resistor, and a largest dimension of the membrane is lessthan 50%; and wherein the ratio of a largest distance between a point ofthe third resistor and a point of the fourth resistor, and a largestdimension of the membrane is less than 50%.

With “external pressure” is meant e.g. air pressure or gas pressure ofthe environment wherein the pressure sensor is located, in contrast to“internal pressure” e.g. caused by the packaging.

By providing the first and second resistor on or adjacent to the sameside portion, whereby the ratio of a largest distance between a point ofthe first resistor and a point of the second resistor, and a largestdimension of the membrane (e.g. the width of a square membrane, or thediameter of a circular membrane) is less than 50%, or even less than25%, meaning in fact that the resistors R1 and R2 are located “closelytogether” relative to the dimensions of the membrane, the temperature ofthese resistors is substantially the same, and hence the ratio of theresistance values R1/R2 of the first and second resistor issubstantially insensitive to temperature variations (over time) at thefirst side portion, and to temperature differences between the firstside portion and any other location of the membrane. Likewise, the ratioof the resistance values R3/R4 is substantially insensitive totemperature variations (over time) at the second side portion, and totemperature differences between the second side portion and any otherlocation of the membrane, in particular the first side portion. Thus, byarranging the resistors as indicated, the accuracy of the bridge isrelatively insensitive (or at least has a reduced sensitivity) to atemperature gradient over the sensor chip, in particular over themembrane.

Since at least one of the first, second, third and fourth resistors hasone or more piezo-resistive element, e.g. one or more piezo-resistivestrips, deformation of the membrane caused by external pressure willcause imbalance of the bridge circuit, and thus the external pressureapplied to the membrane can be measured over the output nodes of thebridge, in a way which is insensitive to a temperature gradient over themembrane. As far as known to the inventors, compensating for temperaturedifferences (e.g. a temperature gradient) over the membrane is not knownin the art. The existence of such a temperature gradient and its impacton the accuracy of the sensor, is probably not even recognized in thefield.

The output signal of the bridge, which can be measured over the outputnodes, is representative for the deformation of the membrane, and hencefor the external pressure.

By locating the resistors of each pair on the same side portion, and“relatively close” together, the influence of a temperature gradientwhich may exist over the membrane is strongly reduced, or even canceled.In other words, the zero-offset due to a temperature gradient over themembrane, is reduced or canceled.

In particular embodiments, the piezo-resistive strips of the firstbridge are completely located on the membrane, although that is notabsolutely required. In fact, simulations have shown that maximumsensitivity of the sensor can be obtained by partially locating thepiezo-resistive strips on the bulk material.

Piezo-resistive strips can be fabricated on silicon devices in knownways, in particular by orienting the strips in a particular way withrespect to the crystal lattice.

In an embodiment, at least two of the first, second, third and fourthresistors comprise one or more elongated piezo-resistive strips arrangedfor measuring deformation of the membrane due to the external pressureto be measured; and whereby the piezo-resistive strips are oriented suchas to cooperate to the imbalance of the bridge when a pressure isexerted on the membrane.

It is an advantage of using at least two piezo-resistive strips, wherebythe strips are oriented such that the individual influences of eachpiezo-resistive element are accumulated in the output voltage. Usingmore than one piezo-resistor increases the sensitivity and the accuracyof the pressure measurement.

This requires however that the resistors are oriented in such a way thatthey cooperate to the imbalance of the bridge. For example, if(referring to the arrangement of FIG. 4) only R1 and R2 would bepiezo-resistive, their piezo-resistive strips need to be orientedsubstantially orthogonal, so that (for p type silicon strips) anincrease of R1 due to pressure is accompanied by a decrease of R2 due tothat same pressure. As another example, if only R1 and R3 would bepiezo-resistive, and R1 and R3 are arranged on adjacent sides of asquare membrane, their piezo-resistive strips would need to be orientedsubstantially parallel. However, if only R1 and R3 would bepiezo-resistive, and R1 and R3 are arranged on opposite sides of asquare membrane, their piezo-resistive strips would need to be orientedorthogonally.

In an embodiment, at least three of the first, second, third and fourthresistors comprise one or more elongated piezo-resistive strips arrangedfor measuring deformation of the membrane due to the external pressureto be measured; and whereby the piezo-resistive strips are oriented suchas to cooperate to the imbalance of the bridge when a pressure isexerted on the membrane.

Using at least three piezo-resistive strips increases the sensitivityand the accuracy of the pressure measurement even more.

In an embodiment, each of the first, second, third and fourth resistorscomprises one or more elongated piezo-resistive strips arranged formeasuring deformation of the membrane due to the external pressure to bemeasured; and whereby the piezo-resistive strips are oriented such as tocooperate to the imbalance of the bridge when a pressure is exerted onthe membrane.

Referring to the arrangement of FIG. 4, the piezo-resistive strips ofthe first, second, third and fourth resistor are chosen such that, whenan external pressure is applied to the membrane, deformation of themembrane would cause the first and third resistance values to increase,while decreasing the second and fourth resistance values, or vice versa,thus the bridge imbalance R1/R2 versus R3/R4 would be maximized, andthus the sensor sensitivity increased.

In an embodiment, the at least one resistor comprising one or moreelongated piezo-resistive strips, comprises at least two or at leastthree piezo-resistive strips connected in series.

By providing at least two or at least three piezo-resistive stripsconnected in series, the resistance value can be increased withouthaving to decrease the doping level. In the case where each of theresistors has at least one piezo-resistive strip, each of the resistorspreferably has at least two or at least three such strips connected inseries. This is especially important when dimensions of the chip becomesmaller due to technology scaling. The piezo-resistive strips of eachindividual resistor are substantially oriented in parallel.

In an embodiment, the second side portion is located substantially orprecisely at 90° angular distance from the first side portion, asmeasured from a center of the membrane.

It is an advantage of embodiments of the present invention where thesecond side portion is located substantially or precisely at 90° withrespect to the first side portion, (e.g. in case of a square membranethis means that the first pair and the second pair are located onadjacent sides), because such a structure has a reduced sensitivity tothe influence of a uniform stress, e.g. a stress parallel to thesubstrate. By this configuration a uniform stress across the membranecauses a common mode voltage shift of the output nodes and not anadditional differential signal.

In an embodiment, the ratio of a largest distance between a point of thefirst resistor and a point of the second resistor, and a largestdimension of the membrane is less than 25%; and the ratio of a largestdistance between a point of the third resistor and a point of the fourthresistor, and a largest dimension of the membrane is less than 25%.

It is an advantage of embodiments of the present invention that thepiezo-resistive strips of the first and second resistor are located“relatively close to each other”. The reason for defining “close” bymeans of said ratio is to unambiguously define what is meant by“relatively close”.

The smaller the distance between the piezo-resistive strips, the smallertheir temperature difference will be, such that it can be assumed thatthe temperature of all strips within one branch of the bridge issubstantially the same, even if there is a temperature differencebetween the branches.

In an embodiment, the membrane is substantially square, and the largestdimension is the width of the square, the first side portion is a firstside of the square, and the second side portion is a second side of thesquare adjacent the first side; and the first resistor and the secondresistor are arranged substantially in the middle of the first side ofthe square; the third resistor and the fourth resistor are arrangedsubstantially in the middle of the second side of the square.

In this embodiment, the pressure sensor has a membrane with a squareshape. When a pressure is exerted on the square membrane, thedeformation is larger in the middle of the sides than near the corners,and larger on the sides than in the center of the membrane, thus byproviding the resistors substantially in the middle of the sides, thesensitivity of the pressure sensor is increased, e.g. maximized.

At the middle of the sides, and in a direction perpendicular to themembrane edge, stress due to the pressure exerted on the membrane istypically about 50% of this maximum value at a distance of about 2 times(2×) the membrane thickness. Therefore the first, second, third andfourth resistor are preferably completely located within a distance of 3times (≦3×) the membrane thickness from the membrane edge, although (inprinciple) it is sufficient that at least one of the piezo-resistivestrips of said resistors is located within that distance.

In an embodiment, the membrane is substantially circular, and thelargest dimension is the diameter of the circle; or the membrane issubstantially rectangular, and the largest dimension is the larger ofthe length and the width of the rectangle; or the membrane issubstantially elliptical, and the largest dimension is the larger of thefirst and the second axis of the ellipse.

These are several examples of membrane shapes, whereby an appropriatedimension of the membrane is specified, however the invention is notlimited to these examples, and membranes having other shapes may also beused, such as e.g. triangular shape, etc.

In an embodiment, the ratio of the resistance of the first resistor andthe resistance of the second resistor lies in the range of 50% to 200%;and the ratio of the resistance of the third resistor and the resistanceof the fourth resistor lies in the range of 50% to 200%, when noexternal stress is applied.

With resistance is meant “electrical resistance”.

It is an advantage to choose the first resistance value approximatelyequal to the second resistance value, because then the voltage at theoutput nodes would be about 50% of the bias voltage applied to thebridge, allowing maximum zero offset in either positive or negativedirection. At the same time, the risk for clipping the output signal tothe supply voltage or to ground, is reduced.

In an embodiment, the second side portion is located at 90° angulardistance from the first side portion as measured from a center of themembrane, and the elongated piezo-resistive strips of the first resistorare oriented orthogonal to the elongated piezo-resistive strips of thesecond resistor; and the elongated piezo-resistive strips of the thirdresistor are oriented orthogonal to the elongated piezo-resistive stripsof the fourth resistor; and the elongated piezo-resistive strips of thefirst resistor are oriented parallel to the elongated piezo-resistivestrips of the third resistor.

This is a particularly interesting arrangement (when using only a singlebridge), which has a reduced sensitivity to temperature gradient overthe membrane, but in additional has a reduced sensitivity to uniformpackage stress.

In another embodiment, the second side portion is located at 180°angular distance from the first side portion as measured from a centerof the membrane, and the elongated piezo-resistive strips of the firstresistor are oriented orthogonal to the elongated piezo-resistive stripsof the second resistor; and the elongated piezo-resistive strips of thethird resistor are oriented orthogonal to the elongated piezo-resistivestrips of the fourth resistor; and the elongated piezo-resistive stripsof the first resistor are oriented orthogonal to the elongatedpiezo-resistive strips of the third resistor.

This is another particularly interesting arrangement (when using only asingle bridge), which has a reduced sensitivity to temperature gradientover the membrane, but unfortunately is still sensitive to uniformpackage stress.

In an embodiment, the semiconductor pressure sensor further comprises asecond bridge circuit comprising a third resistor pair arranged at thefirst side portion of the membrane but outside of the membrane, and afourth resistor pair arranged at the second side portion of the membranebut outside of the membrane; the third resistor pair comprising a fifthresistor connected between the first bias node and a third output node,and a sixth resistor connected between the third output node and thesecond bias node; the fourth resistor pair comprising a seventh resistorconnected between the first bias node and a fourth output node, and aneighth resistor connected between the fourth output node and the secondbias node; at least one of the fifth and sixth and seventh and eighthresistor comprising one or more elongated piezo-resistive stripsarranged at a distance from the membrane edge of at least 4 times (≧4×)the membrane thickness for only measuring stress exerted by packaging onthe semiconductor substrate (and not the pressure exerted on themembrane); circuitry for compensating the value measured by the firstbridge using the value measured by the second bridge.

By locating the third and fourth resistor pairs on the substrate outsidethe membrane, at a distance from the membrane edge of at least 4 times(≧4×) the membrane thickness, e.g. at least 8 times (≧8×) the membranethickness, these strips are only sensitive to package stress, but not todeformation of the membrane due to the external pressure, in contrast tothe first and second resistor pairs, being mainly located on themembrane, within a distance of at most 3 times (≦3×) the membranethickness, which are sensitive to both package stress and the externalpressure to be measured.

By combining, e.g. subtracting the signals from the first and secondbridge, the package stress can be compensated for, or the influencethereof can at least be reduced in the final stress measurement value.

Thus, a semiconductor pressure is provided with a reduced sensitivity tocommon mode temperature, e.g. ambient temperature (due to the firstbridge), and to temperature gradients (due to using resistor pairsarranged “closely together”), and to common mode package stress (due tothe resistor pairs of the second bridge, outside of the membrane), andoptionally also to uniform package stress (e.g. exerted in a directionparallel to the substrate, if the resistor pairs are arranged at about90° angular distance).

In an embodiment, each of the fifth and sixth and seventh and eighthresistor comprise one or more elongated piezo-resistive strips arrangedfor measuring the stress caused by packaging on the semiconductorsubstrate.

As for the first and second resistor pair, a larger signal is obtainedwhen each of the fifth to eighth resistor comprises piezo-resistivestrips, resulting in a more accurate signal.

In an embodiment, the elongated piezo-resistive strips of the fifthresistor and of the sixth resistor are oriented in orthogonaldirections, and the elongated piezo-resistive strips of the fifthresistor are parallel or orthogonal to the elongated piezo-resistivestrips of the first resistor, and the elongated piezo-resistive stripsof the seventh resistor and of the eighth resistor are oriented inorthogonal directions, and the elongated piezo-resistive strips of thefifth resistor are parallel or orthogonal to the elongatedpiezo-resistive strips of the first resistor.

By using four piezo-resistive resistors, and arranging them in thismanner, the imbalance of the bridge is increased (e.g. maximized), andhence the sensitivity of the sensor is increased, e.g. optimized.

In an embodiment, the elongated piezo-resistive strips of each of thefifth, sixth, seventh and eighth resistor have the same dimensions asthe elongated piezo-resistive strips of the first, second, third andfourth resistor respectively.

This has the advantage that the behaviour of the first and of the secondbridge is better matched.

In an embodiment, each of the first, second, third, fourth, fifth,sixth, seventh and eighth resistor have the same number ofpiezo-resistive strips, and the dimensions of all these piezo-resistivestrips are identical.

This has the advantage that the behaviour of the first and of the secondbridge is optimally matched. Preferably in this case the layout of theresistor pairs is as much as possible identical (apart from rotation,translation, mirroring, and/or scaling). It was surprisingly found thatby doing so, there is a very good correlation between the zero-offset ofthe first (inner) bridge and the zero-offset of the second (outer)bridge, so that the compensation of the first bridge can be muchimproved (at least a factor of 2).

In a particular embodiment, the second side portion is located at 90°angular distance from the first side portion as measured from a centerof the membrane, and the elongated piezo-resistive strips of the firstresistor are oriented orthogonal to the elongated piezo-resistive stripsof the sixth resistor; and the elongated piezo-resistive strips of theseventh resistor are oriented orthogonal to the elongatedpiezo-resistive strips of the eighth resistor; and the elongatedpiezo-resistive strips of the fifth resistor are oriented parallel tothe elongated piezo-resistive strips of the seventh resistor, and theelongated piezo-resistive strips of the fifth resistor are orientedparallel to the elongated piezo-resistive strips of the first resistor.

This is a particularly interesting arrangement (when using a doublebridge), which has a reduced sensitivity to temperature gradient overthe membrane, but in additional has a reduced sensitivity to uniformpackage stress, and has an improved zero-offset correction of the firstbridge, thanks to the matching of the piezo-resistors, especially if thelayout of the resistors is the “same” (apart from rotation, translation,and mirroring).

In another particular embodiment, the second side portion is located at180° angular distance from the first side portion as measured from acenter of the membrane, and the elongated piezo-resistive strips of thefifth resistor are oriented orthogonal to the elongated piezo-resistivestrips of the sixth resistor; and the elongated piezo-resistive stripsof the seventh resistor are oriented orthogonal to the elongatedpiezo-resistive strips of the eighth resistor and the elongatedpiezo-resistive strips of the fifth resistor are oriented orthogonal tothe elongated piezo-resistive strips of the seventh resistor; and theelongated piezo-resistive strips of the fifth resistor are orientedparallel to the elongated piezo-resistive strips of the first resistor.

This is another particularly interesting arrangement (when using adouble bridge).

In embodiments, the semiconductor pressure sensor is arranged on a CMOSwafer, whereby the membrane is located in an (100) plane, and at leastone of the piezo-resistive elements is oriented in the <110> direction.

Particular and preferred aspects of the invention are set out in theaccompanying independent and dependent claims. Features from thedependent claims may be combined with features of the independent claimsand with features of other dependent claims as appropriate and notmerely as explicitly set out in the claims.

These and other aspects of the invention will be apparent from andelucidated with reference to the embodiment(s) described hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a semiconductor pressure sensor, known in the art.

FIG. 2 shows a Wheatstone bridge configuration with two branches, eachcomprising two resistors, known in the art.

FIG. 3 shows another semiconductor pressure sensor, known in the art.

FIG. 4 shows the Wheatstone bridge of FIG. 2, with additionalindications of certain aspects relevant for the present invention.

FIG. 5 shows a top view of an example of a layout pattern comprising aresistor pair, and lead-out portions, as can be used in a pressuresensor according to embodiments of the present invention. The resistorpair comprises piezo-resistive strips (dark gray) in close vicinity ofthe membrane edge.

FIG. 6 shows an enlarged view of the piezo-resistive strips of FIG. 5,with an indication of “the largest distance between a point of the firstresistor and a point of the second resistor”.

FIG. 7 shows a variant of the layout pattern of FIG. 5, whereby thelead-out region of the output node lies between the lead-out regions ofthe biasing nodes.

FIG. 8 is a variant of the layout pattern of FIG. 7, whereby eachresistor has only two parallel piezo-resistive strips connected inseries instead of three.

FIG. 9 shows part of a first embodiment of a pressure sensor accordingto embodiments of the present invention, having two resistor pairs usingthe layout pattern of FIG. 5 (or part thereof), located on adjacentsides of a square semiconductor membrane, the two resistor pairs beingconnected in a bridge.

FIG. 10 shows part of a second embodiment of a pressure sensor accordingto embodiments of the present invention, having four resistor pairsusing the pattern of FIG. 5 (or part thereof), two pairs being locatedon the membrane and being connected in a first bridge, and two otherpairs being located outside the membrane, and being connected in asecond bridge, the third and fourth pair being located in close vicinityof the first and second pair respectively.

FIG. 11 shows a variant of the embodiment of the pressure sensor of FIG.9, whereby the first and second resistor pair are located on oppositesides of the square membrane.

FIG. 12 shows a variant of the embodiment of the pressure sensor of FIG.11, whereby the first, second, third and fourth resistor pairs arelocated on opposite sides of the square membrane.

FIG. 13 shows a variant of the embodiment of the pressure sensor of FIG.11, using the layout pattern of FIG. 8 (or part thereof) instead of thepattern of FIG. 5.

FIG. 14 shows an schematic example of radial stress (e.g. caused bypressure) at four locations of the membrane, which stress is typicallycaused by a pressure exerted on the membrane in a directionperpendicular to the substrate.

FIG. 15 shows an schematic example of uniform stress (in this case fromleft to right) at four locations of the membrane, which stress may becaused by packaging.

FIG. 16 shows a variant of the embodiment of the pressure sensor of FIG.9, using the pattern of FIG. 8 (or part thereof) instead of the patternof FIG. 5. The drawings are only schematic and are non-limiting. In thedrawings, the size of some of the elements may be exaggerated and notdrawn on scale for illustrative purposes.

Any reference signs in the claims shall not be construed as limiting thescope.

In the different drawings, the same reference signs refer to the same oranalogous elements.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The present invention will be described with respect to particularembodiments and with reference to certain drawings but the invention isnot limited thereto but only by the claims. The drawings described areonly schematic and are non-limiting. In the drawings, the size of someof the elements may be exaggerated and not drawn on scale forillustrative purposes. The dimensions and the relative dimensions do notcorrespond to actual reductions to practice of the invention.

Furthermore, the terms first, second and the like in the description andin the claims, are used for distinguishing between similar elements andnot necessarily for describing a sequence, either temporally, spatially,in ranking or in any other manner. It is to be understood that the termsso used are interchangeable under appropriate circumstances and that theembodiments of the invention described herein are capable of operationin other sequences than described or illustrated herein.

Moreover, the terms top, under and the like in the description and theclaims are used for descriptive purposes and not necessarily fordescribing relative positions. It is to be understood that the terms soused are interchangeable under appropriate circumstances and that theembodiments of the invention described herein are capable of operationin other orientations than described or illustrated herein.

It is to be noticed that the term “comprising”, used in the claims,should not be interpreted as being restricted to the means listedthereafter; it does not exclude other elements or steps. It is thus tobe interpreted as specifying the presence of the stated features,integers, steps or components as referred to, but does not preclude thepresence or addition of one or more other features, integers, steps orcomponents, or groups thereof. Thus, the scope of the expression “adevice comprising means A and B” should not be limited to devicesconsisting only of components A and B. It means that with respect to thepresent invention, the only relevant components of the device are A andB.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with the embodiment is included in at least oneembodiment of the present invention. Thus, appearances of the phrases“in one embodiment” or “in an embodiment” in various places throughoutthis specification are not necessarily all referring to the sameembodiment, but may. Furthermore, the particular features, structures orcharacteristics may be combined in any suitable manner, as would beapparent to one of ordinary skill in the art from this disclosure, inone or more embodiments.

Similarly it should be appreciated that in the description of exemplaryembodiments of the invention, various features of the invention aresometimes grouped together in a single embodiment, figure, ordescription thereof for the purpose of streamlining the disclosure andaiding in the understanding of one or more of the various inventiveaspects. This method of disclosure, however, is not to be interpreted asreflecting an intention that the claimed invention requires morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive aspects lie in less than allfeatures of a single foregoing disclosed embodiment. Thus, the claimsfollowing the detailed description are hereby expressly incorporatedinto this detailed description, with each claim standing on its own as aseparate embodiment of this invention.

Furthermore, while some embodiments described herein include some butnot other features included in other embodiments, combinations offeatures of different embodiments are meant to be within the scope ofthe invention, and form different embodiments, as would be understood bythose in the art. For example, in the following claims, any of theclaimed embodiments can be used in any combination.

In the description provided herein, numerous specific details are setforth. However, it is understood that embodiments of the invention maybe practiced without these specific details. In other instances,well-known methods, structures and techniques have not been shown indetail in order not to obscure an understanding of this description.

In the present invention, the terms “diaphragm” and “membrane” are usedas synonyms for indicating a region of a semiconductor substrate with areduced thickness as compared to the surrounding substrate material(called “bulk”), adapted to mechanically deform when a pressure to bemeasured is applied thereto.

When in the present invention, reference is made to “largest dimensionof the membrane” or simply “dimension of the membrane”, reference ismade to the length of a side in case the membrane has a substantiallysquare shape, or to the distance between opposite sides in case themembrane has a square shape with rounded corners, or to the diameter incase the membrane is substantially circular, or the length of thelargest axis in case the membrane is substantially elliptical, or to thelarger of the length and the width in case the membrane is substantiallyrectangular, or to the diameter of the inner circle in case the membranehas a regular polygonal shape, such as e.g. a hexagonal or octagonalshape.

The term “thickness of the membrane” has its usual meaning, as can bemeasured in a direction perpendicular to the substrate.

While the circuit of U.S. Pat. No. 4,672,411 (Hitachi), described in thebackground section and illustrated in FIG. 1 has some drawbacks, many ofthe basic principles described therein are also used in the presentinvention. For example, the membrane edges of embodiments of the presentinvention are preferably realized in such a way that maximum stresscaused by the applied pressure is reached in at least two areasperpendicular to the membrane edge and where the membrane edge isoriented in the <110> direction. Anisotropic etching of square membranesin silicon is often used as it creates four of such areas at the middleof the membrane edges due to the anisotropic etch stop on <111> planes.By using other etching methods round membranes would also result in fourof such areas and oval membranes in two of such areas. The stresssensitivity of piezo-resistors also depends on the crystal orientationand the p doped resistors have a maximum change in resistance along the<110> directions, and a minimum change in resistance along the <100>directions, at 45° from the <110> directions. Metal connections causestress in the silicon and due to creep this stress can also change overtime. Therefore a highly doped p doped path is realized between themetal and the piezo-resistive strips. By placing these highly p dopedpaths in the <100> directions at 45 degrees of the <110> directions oneassures that stress from the metal lines does not change the resistanceof these strips.

In order to avoid unnecessary repetition of these basic concepts, thepresent application will not go into further details of crystallographicplanes and directions, and will concentrate on the contribution of thepresent invention over the prior art. The reader may refer to U.S. Pat.No. 4,672,411 for more details. Although other crystallographicdirections may also be used, it is assumed that the membrane of apressure sensor according to the present invention is located in an(100) crystallographic plane of a CMOS wafer, and that thepiezo-resistive strips are located in the <110> direction. Using CMOSwafers allows the combination of the pressure membrane and CMOScircuitry, e.g. at least readout-circuitry, to be integrated on the samewafer.

Before a pressure sensor according to embodiments of the presentinvention is described, first the principles of a Wheatstone-bridgecircuit are explained. Wheatstone-bridge circuits with four resistorsarranged as shown in FIG. 2, are well known in the art. Such circuitsare very well suited for determining an unknown resistor value Rx, whenthree other resistor values R1, R2 and R3 are known, or for measuringsmall resistance changes when all four resistor values are known. Thebridge of FIG. 2 has four resistors R1, R2, R3 and R4 (or Rx). When asupply voltage (e.g. a DC voltage) Vdd and Gnd are applied to the nodesA and C, respectively, a first current will flow from A to C through thefirst branch formed by R1 in series with R2, and a second current willflow through the second branch formed by R3 in series with R4. Adifferential voltage output “Vout” is provided over the nodes D and B,and defined as: Vout=Vd−Vb.

When the bridge is “in balance”, the following formula applies:

R1/R2=R3/R4  (1)

which is equivalent to:

R1×R4=R2×R3  (2)

When the bridge is in balance, the voltage “Vd” at the node D between R1and R2 will be exactly equal to the voltage “Vb” at the node B betweenR3 and R4, and no current will flow in a path between the nodes B and D(e.g. through a galvanometer, indicated by Vg). When one or more of theresistor values R1 to R4 deviate, even slightly, from this balancesituation, the bridge is no longer in balance, and a voltage differenceVout will appear over the nodes D and B, which can be measured in anymanner known in the art, e.g. typically by an amplifier having anamplification factor of about 100 or more. Such a bridge circuit isrelatively insensitive to common mode temperature changes, i.e. when thetemperature of all resistors R1 to R4 increases or decreases with a sameamount, because not the absolute resistance values are important, butonly their ratio, as can be understood from formula (1) above.

In an ideal pressure sensor, the voltage output over the nodes D and Bshould be exactly zero when no pressure difference, further simplyreferred to as “pressure”, is applied to the membrane 2, and ideallythis value remains exactly zero irrespective of the sensor temperaturein absence of said pressure. In practice, however, this output voltagevalue Vg corresponding to zero-pressure, is not exactly zero, and needsto be compensated for, in order to achieve an accurate pressuremeasurement value. This non-zero value is called “zero-offset”, i.e. thevoltage offset value between nodes D and B when no external pressure isexerted on (or applied to) the sensor membrane. There are variousreasons for such zero-offset, e.g. mismatch between the variousresistance values due to imperfections of the semiconductor processing,residual stresses in the membrane due to packaging of the semiconductor(e.g. silicon) die, or an inhomogeneous electric field perpendicular tothe substrate, which modifies the resistors not in the same way(depletion layer changes). While for discrete (thick film) resistors, amismatch between the various resistance values due to semiconductorprocessing may be corrected by laser trimming at the production stage,laser trimming is not possible for piezo resistors that are part of aCMOS circuit. In addition, also several other effects, such as e.g.stress due to packaging and temperature gradient remain.

Various attempts have been made in the art for reducing the zero-offset.For example, FIG. 3 shows a prior art pressure sensor disclosed byHoneywell in EP0083496. It is to be noted that in the illustration inthe present document black lines are added to FIG. 3, to clearlyindicate the position and orientation of the piezo-resistive strips, forreasons that will become clear later. This sensor has a first bridgewith resistors located on the membrane for measuring the pressureexerted on the membrane. This first bridge has a zero-offset due totemperature variations and due to package stress. This offset is reducedby using a second bridge, having four resistors located outside themembrane. This total double bridge sensor provides a pressure value thatis compensated for package stress, however, the compensation is notperfect.

While the problem of compensating for package stress was addressed byHoneywell, as far as known to the inventors, no pressure sensor has beendeveloped so far, that takes into account a temperature difference ortemperature gradient over the substrate, in particular, over themembrane 2. Yet, the inventors found that a temperature difference assmall as 0.1° C. of one of the resistors R1 to R4 would typically causea 1% full scale error. This problem is probably not even recognized inthe field. It is to be noted that this is a different problem fromcompensating against a varying temperature common for all resistors,which problem is inherently solved by using the bridge structure.

The inventors further realised that such a temperature difference (ortemperature gradient) may be hard or even impossible to predict, becauseit may e.g. be caused by the power dissipated by several sub-circuits onthe integrated pressure sensor, and it may even be firmware dependent(e.g. when the sensor is part of an integrated chip with a processorthat activates or deactivates certain sub-circuits, or changes theirclock frequencies). But temperature gradients on the semiconductor, e.g.silicon, die may also be caused by the environment, e.g. when thepressure sensor is exposed to a non-homogeneous and/or time-dependentheat flow.

After realizing the presence of a temperature gradient on the membrane,a closer look at the prior art sensor of FIG. 1 revealed that theresistors are placed relatively far apart from each other at thedifferent membrane edges (the distance between the resistors isapproximately equal to 0.7× the membrane size). On top of thereadout-signal (indicative for the external pressure to be measured), anerror signal is produced in case a temperature gradient is presentacross the membrane. The resistors will be of different values due tothese temperature differences. The error signal increases (e.g. aboutproportionally) with increasing temperature differences of theresistors, and the further the resistors are apart the larger thesetemperature differences will be. In a similar way an error signal isproduced when the residual stress on the resistors (e.g. stress that isnot caused by the external pressure to be measured) is not the same forall resistors, and may even change over time. Such stress can e.g. becaused by forces introduced by the packaging of the sensor. This changein stress can e.g. be caused by plastic deformation of the glue thatbonds the sensor to a surface, plastic deformation of the surface and/orplastic deformation of the protection gel that is often applied. A thirdsource of error can be caused by a non-uniform external electric fieldwhich is not the same for the individual resistors, and again, thefurther the resistors are spaced apart, the more their resistance valueswill differ. Such an electrical field changes the value of a diffusedresistor e.g. as it modifies the insulating depletion layer. Possiblesources can be emission of electric fields from external components nearthe chip, electronics that are integrated on chip or from charge trappedin the material above the piezo resistors. In addition, two or more ofthese phenomena (temperature, package stress, electric field) may occursimultaneously.

Looking for a solution to reduce the inaccuracy caused by a temperaturegradient, the inventors came to the technical insight that the fourresistors R1 to R4 of the Wheatstone bridge of FIG. 2, in fact, need notall have the same temperature for the bridge to be (or remain) inequilibrium, but it suffices that the temperature of the resistors R1and R2 of the first branch are (substantially) the same, and that thetemperature of the resistors R3 and R4 of the second branch are(substantially) the same, as indicated by “Pair1(T1)” and “Pair2(T3) inFIG. 4. In mathematical notation, if Ti represents the temperature ofthe resistor Ri, for i=1 to 4, then, in order for the bridge to be (orremain) in equilibrium, it suffices that T1=T2, and T3=T4, but T1 may besubstantially different from T3. In practice, of course, T1 will not beexactly equal to T2, and T3 will not be exactly equal to D4, but what isimportant is that the temperature difference |T1−T2| in absolute valueis smaller than the temperature difference |T1−T3| in absolute value,preferably at least by a factor of 2, more preferably at least by afactor of 5. For the sake of the discussion however, we will assume thatT1=T2 and that T1 is different from T3. As an example, if the resistancevalues of R1 and R2 both increase with e.g. 2% above their nominalvalue, (e.g. because T1 and T2 both increase with 2° C.) the ratio R1/R2remains unchanged, and hence also the voltage Vd at node D remainsunchanged. If at the same time the resistance values of R3 and R4increase with e.g. 4% above their nominal value (e.g. because T3 and T4both increase with 4° C.), the ratio R3/R4 remains unchanged, hence thevoltage Vb at node B remains unchanged, and thus the bridge remains inbalance despite the temperature difference between T1 and T3. Thisinsight is one of the underlying ideas of the present invention.

The same is true when the bridge is not entirely in equilibrium, i.e.when Vout < >0. The following formulas are applicable when the bridge isnot in balance:

Vout/Vdd=R2/(R2+R1)−R4/(R3+R4)  (3), or

Vout/Vdd=1/(1+R1/R2)−1/(1+R3/R4)  (4)

From equation (4) it can be seen that only the matching within each pairmatters and that not all resistors need to be matched. This insight isexploited in the present invention by placing the two resistors R1 andR2 “close” to each other (compared to the width W of the membrane 2),such that the temperature difference T1 and T2 thereof, in the presenceof a temperature gradient over the membrane 2, is reduced w.r.t. priorart embodiments. Indeed, the effect of a temperature gradient istypically proportional to the distance between the resistors. In theprior art (e.g. FIG. 1 and FIG. 3), the distance between the resistorsis about ½√2 or about 0.7 times the membrane length (or diameter)whereas for the resistor pairs of the present invention this distance ischosen smaller, e.g. smaller than 0.50 times the membrane length ordiameter, e.g. less than 0.35 times the membrane length or diameter,e.g. less than 0.20 times the membrane length or diameter, or e.g. evenless than 0.10 times the membrane length or diameter. Hence thedifference in temperature |T1−T2| is reduced by about a factor 2 (incase of 0.35) or about one order of magnitude (in case of 0.10).Likewise, the resistors R3 and R4 are located “closely” together. Inorder to avoid the relative term “close”, a more exact definition ofwhat is meant by “close”, will be given in relation to FIG. 6.

At the same time, the two pairs themselves need not be located closelytogether, but are preferably located at locations on the membrane with ahigh sensitivity (e.g. near the middle of the side of a squaremembrane). It is advantageous to locate the resistor pairs apart (e.g.on different edges) rather than locating all four resistors together,because in that way the two resistors of each pair can be located closerto those locations on the membrane with a higher sensitivity (e.g incase of a square membrane, the middle of opposite sides). Even moreimportantly, by not locating the four resistors together, it is possibleto distinguish between stress caused by the pressure (to be measured)and stress caused by the package.

A second (optional) idea underlying embodiments of the present inventionhaving at least two piezo-resistive elements, in particular only two oronly three or four piezo-resistive elements, is to orient thosepiezo-resistive elements, e.g. piezo-resistive strips, in such a waythat they “cooperate” to the imbalance of the bridge. when their valuechanges due to pressure. Several examples are described next.

In a first example, R1 and R2 are piezo-resistive, while R3 and R4 arenot. By properly orienting R1 and R2, an external pressure applied tothe membrane would increase the value of R1 while at the same timedecreasing the value of R2, or vice versa. This has the effect that thevalue of Vd at node D changes in the same direction (e.g. decreases) byboth the change of R1 and the change of R2, while the value of Vb atnode B would remain unchanged due to said pressure. Hence, by theirorientation, the resistors R1 and R2 “cooperate” to the imbalance of thebridge. As a second example, if R1 and R3 are piezo-resistive, then R1and R3 should be oriented in such a way that when R1 increases withpressure, R3 decreases, otherwise Vd and Vb would both change in thesame direction, and hence Vout would remain unchanged. As a thirdexample, in case R1 and R4 are piezo-resistive, R1 and R4 should beoriented in such a way that when R1 increases with pressure, that R4also increases, hence Vd at node D would decrease while Vb at node Bwould increase, hence Vout changes. As a fourth example, in case R2 andR4 are piezo-resistive, R2 and R4 should be oriented in such a way thatwhen R2 decreases (hence Vd decreases), R4 increases (hence Vbincreases). As a fifth example, in case all resistors R1 to R4 arepiezo-resistive, then they should be oriented in such a way that when R1increases, then R2 should decrease, R3 should decrease and R4 shouldincrease. The skilled person can easily derive other possiblecombinations in case of two or three piezo-resistive elements, bylooking at the arrows in FIG. 4, either pointing up (e.g. increasingwith pressure) or down (e.g. decreasing with pressure), but the arrowscould also have been inverted. As will be described further, it dependson which edge of the membrane 2 the resistors R1, R2, R3, R4 arelocated, for deciding whether they should be oriented substantially inparallel or substantially orthogonal.

As explained above, although preferred for maximum sensitivity, it isnot absolutely required that all four resistors R1 to R4 have one ormore piezo-resistive elements 8, 9. Indeed, the invention would alsowork if only one of the resistors, e.g. only R1, had a piezo-resistiveelement sensitive to the pressure exerted on the membrane 2. In thatcase the ratio R1(T1,p)/R2(T2) would be sensitive to pressure but(substantially) insensitive to a temperature gradient (provided thatT1≈T2), while the ratio R3(T3)/R4(T4) would be (substantially)insensitive to both pressure “p” and temperature gradient (provided thatT3≈T4). The sensitivity of such a sensor would be approximately fourtimes smaller than the pressure sensor wherein each of the resistors R1to R4 have piezo-resistive elements.

A third aspect underlying the present invention is the “insight” thatpressure on the membrane is not the only cause for stress in thepiezo-resistors. Such additional stress may have the same effect as anapplied pressure, oriented in a direction perpendicular to the membranesurface (resulting in a radially directed stress), but additional stresscan also be oriented in a common direction for all resistors andsubstantially parallel to the substrate surface. Also this stress can bereduced by properly locating the resistors on the membrane, as will bedescribed further.

FIG. 5 shows an embodiment of a possible pattern of a resistor pair P1comprising a first resistor R1 and a second resistor R2, as can be usedin a pressure sensor according to embodiments of the present invention.

In the example shown, the first resistor R1 comprises three elongatedpressure sensitive semiconductor strips 8 a, 8 b, 8 c connected inseries, but more than three or less than three strips may also be used,for example only two strips. These strips 8 a, 8 b, 8 c are made ofsemiconductor material doped with dopants of a first dopant type, e.g. ptype silicon, and are oriented in a first direction Y, e.g.corresponding to a crystal lattice direction of relatively large, e.g.maximum piezo-resistive coefficients. For more information about thepiezo-resistive coefficients, and their relation to the crystal latticedirections, the reader is referred to U.S. Pat. No. 4,672,411, inparticular to FIG. 9 thereof, and the corresponding part of thedescription.

The second resistor R2 comprises three elongated pressure sensitivesemiconductor strips 9 a, 9 b, 9 c connected in series, but more thanthree or less than three strips may also be used. These strips 9 a, 9 b,9 c are made of semiconductor material doped with dopants of the firstdopant type, e.g. p type silicon, and are oriented in a second directionX, substantially orthogonal to the first direction Y, also correspondingto a crystal lattice direction of relatively large, e.g. maximumpiezo-resistive coefficients.

Due to the orthogonal orientation of the (elongated) strips 8 a, 8 b, 8c of the first resistor R1 and the (elongated) strips 9 a, 9 b, 9 c ofthe second resistor R2, an increase of the stress of the strips 8 a, 8b, 8 c due to strain in a direction parallel to the current, wouldentail a similar stress perpendicular to the direction of the current ofthe strips 9 of the second resistor R2. Thus pressure on the membrane 2causing an increase in the electrical resistance of the first resistorR1 would at the same time cause a decrease of the electrical resistanceof the second resistor R2, and vice versa. If fact, this is only truefor p type resistors. While causing a bridge imbalance, this also has asan effect that the current through the bridge is fairly independent ofpressure, because the total resistance of each branch, e.g. (R1+R2) doesnot change ‘much’ with pressure, or more exactly phrased, the change ofthe sum (R1+R2), denoted by |Δ(R1+R2)| is smaller in absolute value thanthe largest of the individual changes |ΔR1| and |ΔR2|.

Electrode lead-out regions 6 are provided for applying bias voltages(e.g. Vdd and Gnd) over the series connection of the resistors R1 andR2, and for measuring the voltage of the intermediate node “D” betweenthe resistors R1 and R2. These lead-out regions 6, as well as “cornerparts” 3 interconnecting the piezo-resistive strips 8 a, 8 b, 8 c andthe strips 9 a, 9 b, 9 c, are made of a heavily-doped layer of the firstdopant type, for instance a heavily-doped p+ type diffused layer. Theyhave a relatively low electrical resistance, and extend in a directionof relatively small piezo-resistive coefficients (in the example shown,preferably at angles of +/−45° with respect to the first and seconddirection Y, X). The lead-out regions 6 extend beyond the edge 21 of themembrane 2, and are in ohmic contact with conductor electrodes, e.g.metal electrodes 4, outside of the membrane 2. Such metal electrodes 4may e.g. comprise aluminum. The reader may notice that the electrodelead-out region 6 connected to node D is not entirely oriented at anglesof +/−45° with respect to the first and second direction Y, X, becausein fact, that is not required for this lead, since there issubstantially no current flowing through this lead. Indeed, the nodes Dand B (only node D is shown in FIG. 5) are typically connected to inputsof an amplifier (not shown) for amplifying the output voltage Vout.

Since the diffused layers of the first dopant type, e.g. p type diffusedlayers, 8 a, 8 b, 8 c, 9 a, 9 b, 9 c constituting the pressure sensingelements have a relatively large, e.g. the maximum, piezo-resistivecoefficient, their electrical resistance is varied greatly by a strainwhich develops due to the deformation of the semiconductor, e.g.silicon, membrane 2. That is, these pressure sensing elements are verysensitive to a pressure or the like. In contrast, since the diffusedlayers are heavily doped with dopants of the first dopant type, e.g.heavily-doped p+ diffused layers, the interconnections 3 and 6 arearranged in orientations of relatively small, e.g. minimumpiezo-resistive coefficients, they are the least sensitive to a pressurechange. By orienting the piezo-resistive strips 8 a, 8 b, 8 c of thefirst resistor R1 close to and orthogonal to the piezo-resistive strips9 a, 9 b, 9 c of the second resistor R2, a pressure exerted on themembrane 2 will have an opposite effect on the electrical resistance ofthe first and second resistors R1, R2, in the sense that, when theresistance of the first resistor R1 increases due to pressure exertedthereon, the resistance of the second resistor R2 decreases, and viceversa, and thus the ratio R1/R2 of the bridge is substantially changeddue to the strain, thereby strongly increasing the sensitivity of thecircuit.

By locating the contacts between the conductive, e.g. metal, electrodes4 and the lead out regions 6 of the first dopant type, e.g. p+ type leadout regions, largely outside the membrane 2, the influence which isexerted on the deformation of the semiconductor, e.g. silicon, membraneby the residual stress developing in the vicinity of the contactportion, and any temperature hysteresis, can be reduced, e.g. minimized.

This aspect is even improved in the layouts shown in FIG. 7 and FIG. 8,where the lead out region 6 of the output node (in the middle of thestructure) is not routed outside of the structure, but is locatedbetween the lead out regions of the biasing nodes. In the structure ofFIG. 7 each resistor R1, R2 contains three piezo-resistive strips. Inthe embodiment of FIG. 8, each resistor contains only twopiezo-resistive strips. But the invention is not limited to theseparticular layouts, and other variants may also be used, for examplerotated, mirrored, scaled and/or stretched versions hereof, or variantshaving a first resistor R1 with three piezo-resistive strips and asecond resistor R2 with only two piezo-resistive strips, or vice versa.

Referring back to FIG. 5, the electrical resistance of the firstresistor R1, (approximately equal to as many times the electricalresistance of one piezo-resistive strip 8 a, 8 b, 8 c as there arestrips in this resistor R1, for instance in the embodiment illustratedthree times in view of R1 comprising three piezo-resistive strips 8 a, 8b, 8 c), is preferably substantially the same as the electricalresistance of the second resistor R2, as is the electrical resistance ofthe third resistor R3 preferably substantially the same as theelectrical resistance of the fourth resistor R4, because in that casethe output voltages Vd and Vb, i.e. the voltage of the node D betweenthe resistors R1 and R2, and of the node B between the resistors R3 andR4 would be substantially halfway between the bias voltages Vdd and Gnd,thus about 50% of the supply voltage Vdd. However, this is notabsolutely required, and the invention would also work if the resistorvalues of R1 and R2 on the one hand, and R3 and R4 on the other hand,would be substantially different.

FIG. 9 shows part of a first embodiment of a pressure sensor accordingto embodiments of the present invention, using two resistor pairs P1, P2having a pattern as shown in FIG. 5, or translated, rotated, mirrored,scaled or stretched versions thereof. The pressure sensor of FIG. 9 hasa membrane 2 with a square shape and four sides S1, S2, S3, S4 of widthW, however the invention is not limited thereto, and would e.g. alsowork with a rectangular, elliptical, circular shape, or other suitableshapes. The sides S1 and S2 are adjacent sides, the sides S1 and S3 areopposite sides. The sensor further comprises a bridge circuit, havingtwo branches between the nodes A and C. The nodes A and C may be biasedby the voltages Vdd and Gnd, in any suitable way known in the art. Thefirst branch comprises a first resistor pair P1 comprising the resistorsR1 and R2 connected in series. The second branch comprises a secondresistor pair P2 comprising the resistors R3 and R4 connected in series.The resistors R1 and R2 are located “close” to one another,substantially in the middle of the side S1, and are “close” to the edgeof the membrane 2. The resistors R3 and R4 are located “close” to eachother, substantially in the middle of the second side S2, and “close” tothe edge of the membrane 2.

In order to quantify that the resistors R1 and R2 of the first pair P1are located “close” to each other (as compared to the size of themembrane 2), a maximum distance L73 defined between a point of the firstresistor R1 and a point of the second resistor R2, in particular definedby a point of the piezo-resistive strips 8 a and a point of thepiezo-resistive strip 9 a of the resistors R1 and R2 is determined, asillustrated in FIG. 6, where said points are indicated by black dots forillustrative purposes. In preferred embodiments of the presentinvention, the ratio of said maximum distance L73 and a dimension of themembrane 2 (in case of a square membrane said dimension would be chosento be the width W of the membrane), i.e. L73/W is less than 50%,preferably less than 40%, preferably less than 35%, preferably less than30%, preferably less than 25%, preferably less than 20%, preferably lessthan 15%, such as e.g. about 10%. In case the membrane 2 has a circularshape, the ratio would be calculated as the length of said maximumdistance L73 over the diameter of the circle. In case the membrane hasan elliptical shape, the ratio would be calculated as the maximumdistance L73 over the larger of the two axes of the ellipse. In case themembrane 2 has a substantially octagonal shape, the ratio would becalculated as the length of said diagonal L73 over the distance betweenopposite sides of the octagonal, etc.

Although not shown in FIG. 5 or FIG. 6, but visible in FIG. 9 to FIG. 13and FIG. 16, the resistors R1, R2, R3, R4 are preferably located aboutin the middle of the sides of the membrane 2, because for a squaremembrane shape, this is where pressure causes maximum tensile stress. Incase of a circular or elliptical membrane, there are no “sides”, but theresistors are preferably located near the edge of the membrane, andsubstantially 90° or 180° apart as seen from the membrane centre, and ina suitable crystallographic position and orientation, in particular, incase of a CMOS wafer, the membrane preferably lies in a (100) plane, andthe piezo-resistive strips are preferably oriented in <110> directions.

As illustrated in FIG. 6, the position of the piezo-resistive strips 8,9 with respect to the membrane edge 21 (indicated in dotted line), inparticular the distance “d1” between the center of the strips 8 and themembrane edge 21, may be chosen to have a maximum of resistance changeof the three strips together (e.g. ΔR1) when a pressure is applied. Fora chosen number of piezo-resistive strips (e.g. three in the embodimentshown), and for chosen dimensions (length and width of the strips, anddistance between the strips), the optimal distance “d1” in terms ofmaximum sensitivity w.r.t. pressure can be determined, e.g. calculatedor simulated or determined in any other way, e.g. via design variation.Likewise, for a chosen number of strips 9, and for chosen dimensionsthereof, an optimal distance “d2” in terms of maximum sensitivity w.r.t.pressure, can be determined. The value of “d2” can be determinedindependent of the value of “d1”, but is dependent on the membrane sizeand membrane thickness T. Finite element modeling may be used todetermine these “optimal” distances. However, the invention would alsowork with sub-optimal positions, since the formula (4) would stillapply. Simulations have shown that such an optimal position may e.g. beobtained by “shifting” the resistive strips 8 about 25% over themembrane edge 21, and by “shifting” the resistive strip 9 c entirelyover the membrane edge 21, but other values for d1 and d2 would alsowork, as long as the first resistor R1 and the second resistor R2 islocated “adjacent” the membrane edge 21, within a distance of at most 3times (≦3×) the membrane thickness T, preferably less than 2.5 times T,e.g. less than 2.0 times T, and substantially near the center of theside of the membrane, because in this region the stress is highest.Simulations have shown that, when a pressure is applied to the membrane2, a stress gradient is established which has its maximum on themembrane 2 close to the edge 21. At the edge there is however no abruptstop of the stress, but it decreases with distance away from the edge 21in the direction of the bulk, and in a direction of the membrane. At adistance of about 2.0 times the membrane thickness T away from the edge,the stress on the bulk silicon is typically still about 50% of themaximum stress.

Referring back to FIG. 9, it can be seen that the resistors R1 and R2 ofthe first pair are thus arranged “close” together (relative to the sizeof the membrane 2), and it can therefore be assumed (or approximated)that the temperatures of the piezo-resistive strips of R1 and R2 are allsubstantially the same, say T1. Likewise, the resistors R3 and R4 of thesecond pair are arranged “close” together, and it can therefore beassumed (or approximated) that the temperatures of the piezo-resistivestrips thereof are substantially the same, say T3, but as the resistorsR3 and R4 of the second pair P2 are located “relatively far” away fromthe resistors R1 and R2 of the first pair P1, the temperature T3 of thesecond pair P2 may be different from temperature T1 of the first pairP1. This technical effect is obtained even if only one of the resistorsR1, R2, R3, R4 are piezo-resistive.

Thus, by locating the strips 8, 9 of the resistors R1 and R2 “relativelyclose” together, more specifically such that the largest possibledistance L73 defined by the strips is only a fraction (e.g. less than50%, preferably less than 20%) of a largest dimension W (length, width,diameter etc.) of the membrane 2, the temperature difference |T1−T2|between the resistors R1, R2 would also only be a fraction of the totaltemperature difference which may exist over the membrane 2. Hence, thesensitivity of the pressure sensor in respect of any temperaturegradient over the membrane 2 is drastically reduced, and thus theaccuracy of the pressure sensor is increased.

It should be mentioned in this respect that it is not important whetherthe resistance of R1, R2 changes linearly with temperature or in anon-linear way, as long as the material of R1 and R2 and theirtemperature is substantially the same, as can be seen from formula (4).Indeed, if both R1 and R2 change according to same non-linear functionwith temperature T, their ratio remains the same. For the sake ofcompleteness, it is recalled that the above described effect (ofinsensitivity of the bridge even if T1 < > T3) is different from thecommon-mode temperature rejection known in the art, whereby thebridge-structure itself is responsible for cancelling the common modetemperature of the resistors R1 to R4, provided they all have the sametemperature.

Still referring to FIG. 9, it can be seen that the first resistor pairP1, comprising R1 and R2, is located adjacent and substantially in themiddle of the first side S1 of the membrane 2, while the second resistorpair P2, comprising R3 and R4, is located adjacent and substantially inthe middle of the second side S2. In the embodiment of FIG. 9 the firstpair P1 and the second pair P2 are located on adjacent sides of themembrane, whereas in the embodiment of FIG. 11, the first pair P1 andsecond pair P2 are located on opposite sides of the membrane 2 (hence180° apart). With “substantially in the middle of a side” is meantwithin an imaginary circle having its centre in the middle of the side,and having a diameter less than 50% of the above mentioned “dimension ofthe membrane” (e.g. the width of a square, the diameter of a circle,etc.), preferably less than 40%, more preferably less than 30%, evenmore preferably less than 20%.

It can further be seen that the orientation of the piezo-resistivestrips of R1 and R2 are orthogonal to each other. The effect hereof isthat, when pressure is exerted in a direction substantiallyperpendicular to the plane XY of the membrane 2 (in the Z-direction), aradial stress will result, as schematically depicted in FIG. 14, whichwill cause the value of R1 to increase, and the value of R2 to decrease(or vice versa). The piezo-resistive strips of R3 and R4 are alsoorthogonal to each other, but in addition, the strips of R3 aresubstantially parallel to those of R1, because then the radial stress onthe side S2 will increase the value of R4 and decrease the value of R3,hence all resistors R1 to R4 are “cooperating” as described above, inrelation to FIG. 4.

In case the membrane 2 would have a circular or elliptical or octagonalshape, the location of the first pair P1 and the location of the secondpair P2 would ideally be chosen at 90° angular distance, as measuredfrom the membrane centre. However, embodiments whereby the angulardistance would be in the range of 70° to 110°, preferably in the rangeof 80° to 100° would also work.

The inventors have discovered that this arrangement of the resistors R1,R2, R3, R4 also reduces the effect of a uniform stress component, e.g. astress-component substantially parallel to the plane of the membrane 2,and oriented for example from left to right as schematically depicted inFIG. 15. Such a stress may e.g. be caused due to the packaging. Howwould the bridge circuit of FIG. 9 react to such a stress? In this casethe value of R2 and R4 would decrease, while the value of R1 and R3would increase, hence, referring to FIG. 4, the value Vd and the valueVb would both decrease, but the value Vout would remain substantiallyunchanged. Hence, the embodiment of FIG. 9 is also substantiallyinsensitive to uniform stress exerted on the membrane 2, in a non-radialdirection.

FIG. 11 shows a variant of FIG. 9, whereby the first and second pair P2of resistors are not arranged at 90° angular distance (in case of asquare membrane this means at adjacent sides), but at 180° angulardistance, (in case of a square membrane this means at opposite sides).This embodiment also has the advantage of having a reduced sensitivityto temperature gradient (because the resistors of each resistor pair are“close” to each other), and of having a substantially maximumsensitivity (because all four resistors R1 to R4 have piezo-resistiveelements, and the piezo-resistive elements are oriented so as to“cooperate” to the imbalance of the bridge when an external pressure isapplied, resulting in a radial stress component (see FIG. 14), andbecause the resistor pairs are located at locations of maximumsensitivity on the membrane. Note however that in contrast to theembodiment of FIG. 9, in this case the strips of R1 and R4 are orientedin parallel (as opposed to orthogonal in FIG. 9), because by doing so,an external pressure resulting in the radial stress pattern of FIG. 14,would cause an increase of R1 and R4, while causing a decrease of R2 andR3.

A disadvantage of this arrangement however is that this sensor does notsubstantially cancel uniform stress in a direction substantiallyparallel to the substrate, e.g. as depicted in FIG. 15. Indeed, such astress pattern would increase the value of R1 and R4 and decrease thevalue of R2 and R3, just like the radial stress pattern due to externalpressure would. As a result a change in package stress will beinterpreted as a change in applied pressure.

FIG. 10 shows a second embodiment of a pressure sensor according to thepresent invention. Most or all of what has been said for the pressuresensor of FIG. 9 also applies to the pressure sensor of FIG. 10. Inaddition to the membrane 2 and the first bridge (comprising P1 and P2)shown in FIG. 9, the pressure sensor of FIG. 10 further comprises asecond bridge (comprising P3 and P4). The second bridge is preferablybiased by the same bias voltage Vdd and ground Gnd as the first bridge,although that is not absolutely required. The second bridge comprisestwo branches, one branch comprising a third resistor pair P3, the otherbranch comprising a fourth resistor pair P4. The third resistor pair P3comprises two resistors R5 and R6 connected in series, the fourthresistor pair P4 comprises two resistors R7 and R8 connected in series.A third output “Ve” is provided at the node E between the fifth andsixth resistor R5 and R6. A fourth output “Vf” is provided at the node Fbetween the seventh and eighth resistor R7, R8. The output voltages Vfand Ve at the nodes E and F provide the differential output voltage ofthe second bridge.

The resistors R1, R2, R3, R4 are located adjacent to and substantiallyin the middle of the first and second side S1, S2 of the membrane 2, asdescribed above.

The resistors R5, R6, R7, R8 of the third and fourth resistor pair P3,P4 are located outside the membrane 2, on the bulk material, and are notintended for measuring deflections of the membrane 2, but for measuringstrain due to packaging. As already indicated above, in order to besubstantially insensitive of the stress exerted upon the membrane 2, theresistors R5 to R8 are preferably located at a distance from themembrane edge, which is at least 4.0 times the membrane thickness T,e.g. at least 6 times T, e.g. about 10 times T. It is noted that thetemperature of resistor R5 should be substantially equal to thetemperature of R6, say T5, which according to aspects of the presentinvention is obtained by locating R5 relatively close to R6, but thetemperature of resistor R5 may be different from the temperature of R1.

By using the same (or a similar, e.g. rotated, translated, mirrored)pattern as shown in FIG. 5 or FIG. 7 or FIG. 8, the piezo-resistivestrips of R5 and R6 are located “closely together” relative to themembrane size (using the same formula L73/W), and hence the temperatureof the fifth and sixth resistors R5, R6 can be considered to besubstantially the same, say T5. Likewise the temperature of the seventhand eighth resistor R7, R8 can be considered substantially the same. Inmathematical notation, if Ti represents the temperature of resistor Ri(for i=5 to 8), then it can be assumed (or at least approximated) thatT5=T6 and T7=T8, but T5 can be substantially different from T7 withoutunbalancing the bridge. Thus by organizing the resistors of the second(outer) bridge in pairs (rather than as individual resistors as is donein the prior art), also the second bridge is insensitive to atemperature gradient, which is a major advantage over the prior art,when using the output of the second bridge to correct the output of thefirst bridge.

Because the thickness T of the membrane 2, typically in the order of 10to 100 micrometer is usually much smaller, e.g. at least ten timessmaller than the size of the membrane (e.g. a membrane width in therange of 200 to 2000 micrometer), the third resistor pair P3 is locatedrelatively “close” to the first resistor pair P1, and the fourthresistor pair P4 is located relatively “close” to the second resistorpair P2, such that the pressure sensed by the third resistor pair P3 dueto the packaging is substantially the same as the pressure exerted bythe package on the first resistor pair P1, and the pressure sensed bythe fourth resistor pair P4 due to the packaging is substantially thesame as the pressure exerted by the package on the second resistor pairP2.

Thus the value measured by the first (inner) bridge is indicative forthe external pressure and package stress, while the value measured bythe second bridge is indicative for the package stress only. If anidentical layout is chosen for the resistors of the first and the secondbridge, and if the same bias voltages are chosen for the first andsecond bridge, the value of the second bridge can be subtracted from thevalue of the first bridge to compensate for package stress. But theinvention is not limited thereto, and in general, the value of thesecond bridge would be proportional to the package stress, and afraction of said value can be subtracted from the output of the firstbridge to compensate the zero-offset against package stress.

Although the use of a second bridge in an attempt to compensate foroffset error due to package stress is already mentioned in the prior art(see EP0083496A2), experiments have shown that the offset compensationof the first bridge by the second bridge organized in the manner asdisclosed in the prior art (with individual resistors distributed on thefour sides of the membrane and the bulk), does not work very well, andis sensitive to a temperature gradient.

It was found that, when the resistors of each branch of the two bridgesare organized in pairs, as described in the present invention, and asshown for example in FIG. 10 and FIG. 12, the matching between the first(inner) bridge measuring the pressure of the membrane and the second(outer) bridge measuring only the package stress is at least 3.0 timesbetter when the bridges comprises resistor pairs rather than individualresistors, which is a major improvement.

It is believed that one of the underlying reasons why the matching ofthe bridges organised in pairs as described herein is significantlybetter than the matching of the prior art bridges, is mainly related tothe fact that the distance between the piezo-resistive strips within thepairs is much shorter than the distance between piezo resistive stripsof the classical bridges, however, the inventors do not wish to be boundby any theory.

By locating the third pair P3 “close” to the first pair P1,automatically also the temperature of the resistors R1, R2, R5 and R6will be substantially the same (thus T1=T2=T5=T6), although that is notabsolutely required, it suffices that T1=T2 and that T5=T6. As mentionedabove, the main reason for locating the third pair P3 close to the firstpair P1 is to match the package stress as good as possible. Since theresistors R1 to R4 are located on the membrane 2, (or more correctlystated: a major portion of R1 and R4 is located on the membrane) theyare sensitive to pressure exerted on the membrane 2 as well as topressure exerted by the package. In contrast, since the resistors R5 toR8 are located “sufficiently far” outside the membrane 2, e.g. at least4.0 times (≧4×) the membrane thickness T away from the membrane edge 21,they are only sensitive to the pressure exerted by the package. Hence,the second bridge comprising the resistors R5 to R8 can be used todetermine the common mode pressure exerted by the package on thesubstrate, which common mode pressure can be used to compensate thepressure value obtained from the first bridge, using known methods.

In practice, a trade-off needs to be made with respect to the positionof the third and fourth resistor pair P3, P4 in relation to the firstresp. second resistor pairs P1, P2: if P3 is located “too close” to themembrane edge (and thus to P1), it provides a better indication (highercorrelation) of the package pressure exerted upon the resistors of P1and P2, but P3 will also be more sensitive to the external pressure onthe membrane. If P3 is “too far” from the membrane edge, it will besubstantially insensitive to the external pressure to be measured by thefirst bridge, but the package stress experienced by P3 may deviate morefrom the package stress experienced by P1 (lower correlation). As a ruleof thumb, the third and fourth resistor pairs P3, P4 may e.g. be locatedat a distance equal to about 4.0 times (4×) to about 10.0 times (10×)the membrane thickness T.

The end result is that the pressure sensor of FIG. 10 is able toaccurately measure the pressure exerted on the membrane 2, with a highsensitivity (because of 4 piezo-resistors being used), in a manner whichis independent of the common mode temperature (by using bridge circuits,whereby only the ratio of resistor values is important, not theirabsolute values), with a reduced sensitivity to package stress (due topresence of and compensation by the second bridge, but also due to the90° angular distance between the first & third pair and the second &fourth pair), and with a reduced sensitivity to a temperature gradientover the chip (due to the close positioning of the two-resistors of eachpair within each bridge).

FIG. 12 shows a variant of FIG. 10, whereby the resistor pairs P1 andP2, and P3 and P4 are located on opposite sides of the membrane 2instead of on adjacent sides. This embodiment can also be seen as avariant of FIG. 11, whereby a third and fourth resistor pair are addedoutside of the membrane. The embodiment of FIG. 12 has the sameadvantages as that of FIG. 10, except for the disadvantage of notreducing the uniform stress in a plane parallel to the substrate, as wasdescribed above in relation to FIG. 15.

In another variant (not shown) of the pressure sensor of FIG. 9, thepressure sensor would have a second bridge with two resistor pairs P3and P4, located mainly on the membrane 2, on the third and fourth sideS3, S4. Such a pressure sensor would measure the pressure exerted on themembrane 2 at four locations instead of only two. Such a second bridgewould normally provide the same or similar values than the first bridge,and hence may be used for self-test or reliability-check (e.g. bycomparing the values of both bridges), or the values may be summed oraveraged for compensating local imperfections, or for increasedaccuracy. However, such a second bridge would not compensate forradially oriented package stress (because it does not have resistorpairs on the bulk material), but it would compensate for uniform packagestress (because the resistor pairs of each bridge are at an angulardistance of 90°).

In a further variant of the pressure sensor just described, the pressuresensor may have a third and a fourth bridge, located outside of themembrane for compensating radial package stress, similar to theembodiment of FIG. 10. If fact, the invention would also work if thefourth bridge were omitted.

FIG. 13 shows a variant of the embodiment of FIG. 11 having a circularmembrane 2, and having the layout structure of the resistor pairs ofFIG. 8. Everything which was said for the embodiment of FIG. 11 is alsoapplicable here, except that in this case each resistor has twopiezo-resistive elements instead of three, and that the membrane edge isnot straight. As can be seen, the resistor pairs are arranged at 180°angular distance, as seen from the center of the membrane.

As was discussed for FIG. 11, and shown in FIG. 12, variants of theembodiment of FIG. 13 may also have a second bridge located on the bulk,for measuring and compensating package stress, or located on themembrane for redundancy reasons or for improved accuracy (by averaging,or selecting the circuit with the best performance during calibration).

FIG. 16 shows a variant of the embodiment of FIG. 9 having a circularmembrane 2, and having the layout structure of the resistor pairs ofFIG. 8. Everything which was said for the embodiment of FIG. 9 is alsoapplicable here, except that in this case each resistor has twopiezo-resistive elements instead of three, and that the membrane edge isnot straight. As can be seen, the resistor pairs are arranged at 90°angular distance, as seen from the center of the membrane.

As was discussed for FIG. 9, and shown in FIG. 10, variants of theembodiment of FIG. 16 may also have a second bridge located on the bulk,for measuring and compensating package stress, or located on themembrane for redundancy reasons or for improved accuracy (by averaging,or selecting the circuit with the best performance during calibration).

REFERENCES: 2 membrane 21 membrane edge 3 corner parts 4 metal electrode6 electrode lead-out regions 73 largest distance 8 piezo-resistive stripof 9 piezo-resistive strip of first resistor second resistor 10piezo-resistive strip of 11 piezo-resistive strip of third resistorfourth resistor P1 first resistor pair R1 first resistor S1 first sideof square W width of the square membrane membrane T membrane thicknessVdd supply voltage Gnd ground voltage

1-21. (canceled)
 22. A semiconductor pressure sensor for measuring anexternal pressure exerted on the sensor, comprising: a membrane as partof a semiconductor substrate for being deformed due to the externalpressure, having a membrane edge and a membrane thickness; a firstbridge circuit comprising a first resistor pair located on or adjacentto a first side portion of the membrane, and a second resistor pairlocated on or adjacent to a second side portion of the membrane; thefirst resistor pair comprising a first resistor connected between afirst bias node and a first output node, and a second resistor connectedbetween the first output node and a second bias node; the secondresistor pair comprising a third resistor connected between the firstbias node and a second output node, and a fourth resistor connectedbetween the second output node and the second bias node; at least one ofthe first and second and third and fourth resistor comprising one ormore elongated piezo-resistive strips arranged for measuring deformationof the membrane due to the external pressure to be measured; wherein theratio of a largest distance between a point of the first resistor and apoint of the second resistor, and a largest dimension of the membrane isless than 50%; and wherein the ratio of a largest distance between apoint of the third resistor and a point of the fourth resistor, and alargest dimension of the membrane is less than 50%.
 23. Thesemiconductor pressure sensor of claim 22, wherein at least two of thefirst, second, third and fourth resistors comprise one or more elongatedpiezo-resistive strips arranged for measuring deformation of themembrane due to the external pressure to be measured; whereby the one ormore piezo-resistive strips are oriented such as to cooperate to theimbalance of the bridge when a pressure is exerted on the membrane. 24.The semiconductor pressure sensor of claim 23, wherein at least three ofthe first, second, third and fourth resistors comprise one or moreelongated piezo-resistive strips arranged for measuring deformation ofthe membrane due to the external pressure to be measured; whereby theone or more piezo-resistive strips are oriented such as to cooperate tothe imbalance of the bridge when a pressure is exerted on the membrane.25. The semiconductor pressure sensor of claim 24, wherein each of thefirst, second, third and fourth resistors comprises one or moreelongated piezo-resistive strips arranged for measuring deformation ofthe membrane due to the external pressure to be measured; whereby theone or more piezo-resistive strips are oriented such as to cooperate tothe imbalance of the bridge when a pressure is exerted on the membrane.26. The semiconductor pressure sensor according to claim 22, wherein theat least one resistor comprising one or more elongated piezo-resistivestrips, comprises at least two piezo-resistive strips connected inseries.
 27. The semiconductor pressure sensor according to claim 22,wherein the second side portion is located substantially or precisely at90° angular distance from the first side portion, as measured from acenter of the membrane.
 28. The semiconductor pressure sensor accordingto claim 22, wherein the ratio of a largest distance between a point ofthe first resistor and a point of the second resistor, and a largestdimension of the membrane is less than 25%; and wherein the ratio of alargest distance between a point of the third resistor and a point ofthe fourth resistor, and a largest dimension of the membrane is lessthan 25%.
 29. The semiconductor pressure sensor according to claim 22,wherein the membrane is substantially square, and the largest dimensionis the width of the square, the first side portion is a first side ofthe square, and the second side portion is a second side of the squareadjacent the first side; and the first resistor and the second resistorare arranged substantially in the middle of the first side of thesquare; the third resistor and the fourth resistor are arrangedsubstantially in the middle of the second side of the square.
 30. Thesemiconductor pressure sensor according to claim 22, wherein themembrane is substantially circular, and the largest dimension is thediameter of the circle; or the membrane is substantially rectangular,and the largest dimension is the larger of the length and the width ofthe rectangle; or the membrane is substantially elliptical, and thelargest dimension is the larger of the first and the second axis of theellipse; the membrane is substantially octagonal, and the largestdimension is the distance between opposite sides of the octagonal. 31.The semiconductor pressure sensor according to claim 22, wherein theratio of the resistance of the first resistor and the resistance of thesecond resistor lies in the range of 50% to 200%; and the ratio of theresistance of the third resistor and the resistance of the fourthresistor lies in the range of 50% to 200%.
 32. The semiconductorpressure sensor according to claim 22, wherein: the second side portionis located at 90° angular distance from the first side portion asmeasured from a center of the membrane, and the elongatedpiezo-resistive strips of the first resistor are oriented orthogonal tothe elongated piezo-resistive strips of the second resistor; and theelongated piezo-resistive strips of the third resistor are orientedorthogonal to the elongated piezo-resistive strips of the fourthresistor; and the elongated piezo-resistive strips of the first resistorare oriented parallel to the elongated piezo-resistive strips of thethird resistor.
 33. The semiconductor pressure sensor according to claim22, wherein: the second side portion is located at 180° angular distancefrom the first side portion as measured from a center of the membrane,and the elongated piezo-resistive strips of the first resistor areoriented orthogonal to the elongated piezo-resistive strips of thesecond resistor; and the elongated piezo-resistive strips of the thirdresistor are oriented orthogonal to the elongated piezo-resistive stripsof the fourth resistor; and the elongated piezo-resistive strips of thefirst resistor are oriented orthogonal to the elongated piezo-resistivestrips of the third resistor.
 34. The semiconductor pressure sensoraccording to claim 22, further comprising: a second bridge circuitcomprising a third resistor pair arranged at the first side portion ofthe membrane but outside of the membrane, and a fourth resistor pairarranged at the second side portion of the membrane but outside of themembrane; the third resistor pair comprising a fifth resistor connectedbetween the first bias node and a third output node, and a sixthresistor connected between the third output node and the second biasnode; the fourth resistor pair comprising a seventh resistor connectedbetween the first bias node and a fourth output node, and an eighthresistor connected between the fourth output node and the second biasnode; at least one of the fifth and sixth and seventh and eighthresistor comprising one or more elongated piezo-resistive stripsarranged at a distance from the membrane edge of at least four times themembrane thickness for only measuring stress exerted by packaging on thesemiconductor substrate; circuitry for compensating the value measuredby the first bridge using the value measured by the second bridge. 35.The semiconductor pressure sensor of claim 34, wherein each of the fifthand sixth and seventh and eighth resistor comprise one or more elongatedpiezo-resistive strips arranged for measuring the stress caused bypackaging on the semiconductor substrate.
 36. The semiconductor pressuresensor of claim 35, wherein the elongated piezo-resistive strips of thefifth resistor and of the sixth resistor are oriented in orthogonaldirections, and wherein the elongated piezo-resistive strips of thefifth resistor are parallel or orthogonal to the elongatedpiezo-resistive strips of the first resistor; the elongatedpiezo-resistive strips of the seventh resistor and of the eighthresistor are oriented in orthogonal directions, and wherein theelongated piezo-resistive strips of the fifth resistor are parallel ororthogonal to the elongated piezo-resistive strips of the firstresistor.
 37. The semiconductor pressure sensor according to claim 34,wherein each of the first, second, third, fourth, fifth, sixth, seventhand eighth resistor have the same number of piezo-resistive strips, andwherein the dimensions of all these piezo-resistive strips areidentical.
 38. The semiconductor pressure sensor according to claim 34,wherein: the second side portion is located at 90° angular distance fromthe first side portion as measured from a center of the membrane, andthe elongated piezo-resistive strips of the first resistor are orientedorthogonal to the elongated piezo-resistive strips of the sixthresistor; and the elongated piezo-resistive strips of the seventhresistor are oriented orthogonal to the elongated piezo-resistive stripsof the eighth resistor; and the elongated piezo-resistive strips of thefifth resistor are oriented parallel to the elongated piezo-resistivestrips of the seventh resistor, and the elongated piezo-resistive stripsof the fifth resistor are oriented parallel to the elongatedpiezo-resistive strips of the first resistor.
 39. The semiconductorpressure sensor according to claim 34, wherein: the second side portionis located at 180° angular distance from the first side portion asmeasured from a center of the membrane, and the elongatedpiezo-resistive strips of the fifth resistor are oriented orthogonal tothe elongated piezo-resistive strips of the sixth resistor; and theelongated piezo-resistive strips of the seventh resistor are orientedorthogonal to the elongated piezo-resistive strips of the eighthresistor; and the elongated piezo-resistive strips of the fifth resistorare oriented orthogonal to the elongated piezo-resistive strips of theseventh resistor; and the elongated piezo-resistive strips of the fifthresistor are oriented parallel to the elongated piezo-resistive stripsof the first resistor.
 40. The semiconductor pressure sensor accordingto claim 22, arranged on a CMOS wafer, whereby the membrane is locatedin an plane, and at least one of the piezo-resistive elements isoriented in the <110> direction.
 41. A semiconductor device comprising asemiconductor pressure sensor according to claim 22.